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Basilar-membrane oscillations.

Dear colleagues,

Sorry, one more posting on the stiffness of the basilar membrane.

In my message of March 27, I 
mentioned the guinea-pig BM oscillation frequency of 2.3 kHz measured by Mammano and Ashmore (1993), "Reverse 
transduction measured in the isolated cochlea by laser Michelson interferometry", Nature 365, 838-841. How much higher 

would the frequency be if the liquid above and below the partition were removed?

One of my wine glasses when empty 
oscillates at ~523 Hz. If it is filled with water, the frequency drops to ~311 Hz, i.e., by a major sixth. If the glass 
is completely under water, the frequency is ~208 Hz, lower than when empty by as much as a major tenth.

A tuning fork, 
however, sinks from 440 Hz to ~415 Hz when immersed, i.e., by a semitone only.

I believe that in these cases, and also 
in the mentioned guinea pig experiment, evanescent liquid-pressure waves occur. In those, the liquid particles move 
back and forth (whereas in travelling surface waves they move on elliptical trajectories). The drop in oscillation 
frequency of resonators by immersing is severe if the streamlines of the evanescent waves are long. In the mentioned 
guinea-pig experiment, at the beginning of the rectangular electric-current pulse, the BM was raised at the pipette 
location (pipette diameter 5 micro-m), and probably was lowered at places more basal and apical by 30 micro-m or so. 
The typical streamline length (approximately half-circular, from raised-BM place to lowered-BM place) may have been ~50 
micro-m. The liquid on both sides of the partition thus may have increased the effective BM surface mass density from 
~0.1 kg / m^2 to ~0.2 kg / m^2, and so decreased the BM resonance frequency by a factor of ~sqrt(0.5) = 0.7, i.e. by 
(very roughly) about half an octave.  

An extrapolation of the exponential guinea-pig BM-resonator map that I 
presented in Fig. 3 of "Old and New Cochlear Maps",  Canadian Acoustics Vol. 37, No. 3 (2009) 174-175, up to x = 11 mm 
from base, yields a frequency of 3.7 kHz, greater than the mentioned experimental result of 2.3 kHz by about a minor 


Reinhart Frosch,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Sommerhaldenstr. 5B,
CH-5200 Brugg.

0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .